Question

The value of `sin^-1(cos  (53pi)/5)` is ______ 

पर्याय

• `(-3pi)/5`

• `(-pi)/10`

• `(3pi)/5`

• `pi/10`

Answer 1

The value of `sin^-1(cos  (53pi)/5)` is `underline((-pi)/10)`.

Explanation:

`cos  (53pi)/5 = cos((50pi)/5 + (3pi)/5)`

= `cos(10pi + (3pi)/5)`

= `cos  (3pi)/5`

= `sin (pi/2 - (3pi)/5) = sin((-pi)/10)`

∴ `sin^-1(cos  (53pi)/5) = sin^-1(sin  (-pi)/10) = (-pi)/10`